Question

Fig. shows a thin $50cm$ long rod resting on two metallic supports in a uniform magnetic field of $0.45T$. Find the maximum voltage which can be applied without breaking the circuit : Mass of the rod is $750g$. Take $g=10m{s}^{-2}$

• A. $83.3V$
• B. $8.33V$
• C. $833V$
• D. $0.833V$

Answer 1

The correct option is A $83.3V$

Let $V$ be the voltage applied.
The current in the circuit is $I=\frac{V}{R}$
At max voltage applied, the upward magnetic force experienced by the rod is balanced by the weight of the rod.
$F_{mag}=ILB=mg$ where $mg$ is the weight of the rod, $L$ is the length of the rod and $B$ is the applied magnetic field.
Substituting for $I$
$\therefore \frac{V}{R}LB=mg$
$\Rightarrow V=\frac{mgR}{LB}=\frac{750\times {10}^{-3}\times 10\times 25}{50\times {10}^{-2}\times 0.45}=83.3V$